Sarra BoudaoudLemnaouar Zedam2021-03-292021-03-292021http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/24091In this paper, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of intuitionistic fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal intuitionistic fuzzy ideal (resp. filter) coincides with an intuitionistic fuzzy down-set (resp. up-set) generated by an intuitionistic fuzzy singleton. Afterwards, for a given intuitionistic fuzzy set, we introduce two intuitionistic fuzzy sets: its intuitionistic fuzzy down-set and up-set, and we investigate their interesting properties. Keywords: lattice, intuitionistic fuzzy set, principal intuitionistic fuzzy ideal, principal intuitionistic fuzzy filter. 2010 Mathematics Subject Classification: 03E72, 06B23, 47H10.Article